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31 Oct 2007: Prove that every r n Latin rectangle may be extended to an n n Latin square.7. ... Show that a graph G (with |G| > k) is k-connected ifand only if there is an a-B fan for every B V (G) with |B| = k and every vertex

9 Apr 2007: 9). holds for every real k > 1/2. Furthermore,. ν̂n (Ut,B) G,. ... 13). 420 R. Nickl. for every real k > 1/2. Furthermore,. ν̂n (Us,B) G,.

30 Jul 2007: 5(b) respectively.Although measurements of strain were obtained every 10 s,Fig. ... 5(a) shows strains only every 30 s and Fig. 5(b) every50 s for the sake of clarity.

3 Jun 2007: The domain is regular for the Dirichlet problem if there is a solution to theDirichlet problem for every continuous function b : R. ... Then B is continuous on and harmonic on. Since b is not constant, neither isB, and so the maximum principle shows that

31 Oct 2007: Suppose that X is reg-ular. Then for every j the specialisation map. ... Then. (i) for every a > 0 and every b d 1, K(b)a Z = 0; and.

11 Mar 2007: 2κ. ), and a two-colouring of[K]2 making every unordered pair red or blue. ... But for suchan α there exists a unique F 2ω1 with α S(F|β) for every β < ω1.

20 Apr 2007: If θ πmod 2π, then every vector in R2 {0} is an eigenvector with eigenvalue1. ... Still more informally, f is injective if different points go to different pointsand f is surjective if it hits every point in B.

5 Oct 2007: b) Use (a) to show that every finitely presented group is the fundamental groupof some space. ... many homotopy classes of maps from X to Y. (b) If m < n, then every map Sm Sn is homotopic to a constant map.

28 May 2007: Show that every orientation preserving isometryof the hyperbolic metric on B3 is an extension of a Möbius transformation. ... State Jørgensen’s inequality, and deduce that not every two-generator subgroup G = 〈A, B〉 ofMöbius transformations is

21 Nov 2007: 6. Show that every graph G has a partition of its vertex-set as X Y such that the numberof edges from X to Y is at least 1. ... 11. Let G be a graph in which every edge is in a unique triangle and every non-edge is adiagonal of a unique 4-cycle.